Answer:
B(2 pi r) = uo i = uo (J pi r^2)
Magnetic field, B = μo Jr/2
Explanation:
The magnitude of the magnetic field inside the wire at a distance r1 < R inside the wire is;
B = ½μ_o × Jr
We want to find the magnitude of the magnetic field inside the wire at a distance r1 < R.
The formula for Magnetic field at a distance r located inside a conductor of radius R is given by Ampere's circuital law as;
B × 2πr = μ_o × Jπr²
Where;
B is magnitude of magnetic field
μ_o is a constant known as magnetic permeability
J is current density
Thus;
B × 2πr = μ_o × Jπr²
πr will cancel out from both sides to give;
2B = μ_o × Jr
B = ½μ_o × Jr
Thus, in conclusion them magnitude of the magnetic field is ½μ_o × Jr
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